I've not read the whole thread, so forgive me if I've repeated something someone else said. Looking at this, it's an ideal application for a "buck regulator". The problem you have is the relatively high power dissipation dropping from 12 to 2ish volts at 270mA.
That's always going to be 2.7 watts in any linear situation. Its not that you can't get a resistor or transistor to handle that, but it's wasteful – especially if you're using a 12V battery.
You can get a buck regulator ready made circuit from ebay, but you can make one too. Broadly it is an oscillator which switches a pass transistor through a diode and an inductor in a PWM fashion. You could use a 555 timer for the oscillator. There is a feedback loop and an error amplifier which are used to control the mark space ratio of the transistor drive. The error amplifier is just a simple op amp, and the transistor drive is a comparator.
If the voltage is too high then the transistor tends more off than on. If the voltage is too low then the transistor tends more on than off. The inductor smooths the output jiggles into a DC voltage.
By only allowing through the required charge, and switching very quickly, the resistive losses are eliminated. If you build the buck regulator from discrete components, it's quite a complicated task. If you buy a buck regulator chip you can just follow the instructions on the datasheet and it will work fine.
An example device is MC33063 which can be used in buck, boost and inverting configurations. It's a £0.40 8 pin part, easily available everywhere despite the chip shortage.
Edited By Andy Ash on 10/11/2022 01:45:52